Statements that share an explanation tend to lend inductive support to one another. For example, being told that Many furniture movers have a hard time financing a house increases the judged probability that Secretaries have a hard time financing a house. In contrast, statements with different explanations reduce one another s judged probability. Being told that Many furniture movers have bad backs decreases the judged probability that Secretaries have bad backs. I pose two questions concerning such discounting effects. First, does (...) the reduction depend on explanations being mutually incompatible or does it occur when explanations are deemed irrelevant to one another? I found that a small discounting effect occurred with statements that were blatantly unrelated. However, the discounting effect also depended on a factor external to the argument being judged; the composition of the argument set. Second, are explanation effects attributable to changes in the belief afforded statements or to response-specific changes resulting from misunderstanding of the probability rating task or response bias? The results implicate changes in belief. Prior belief influenced conditional probability more than argument strength judgements, as it would if participants understood the tasks in the same way as the experimenter. Also, conditional probability true and false judgements were complementary, suggesting no response bias. (shrink)